Problem: Solve for $z$ : $-29 = 12 + z$
Solution: Subtract $12$ from both sides: $ \begin{eqnarray} \\ \hphantom{-29 {- 12}} &\hphantom{=}& \hphantom{z} \\ -29 &=& 12 + z \\ \\ {-12} && {-12} \\ \end{eqnarray} $ $ \begin{eqnarray} \\ -29 {- 12} &=& z \\ \end{eqnarray} $ Simplify. $ z = -41$